Weak type estimates for singular integrals related to a dual problem of Muckenhoupt-Wheeden
A well known open problem of Muckenhoupt-Wheeden says that any Calderón-Zygmund singular integral operator T is of weak type (1, 1) with respect to a couple of weights (w, Mw). In this paper we consider a somewhat “dual” problem: sup λ>0 λw x ∈ R n : |T f(x)| Mw > λ ≤ c Z Rn |f| dx. We prove a...
| Authors: | , , |
|---|---|
| Format: | article |
| Status: | Versión aceptada para publicación |
| Publication Date: | 2009 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/42363 |
| Online Access: | http://hdl.handle.net/11441/42363 https://doi.org/10.1007/s00041-008-9032-2 |
| Access Level: | Open access |
| Keyword: | Calderón-Zygmund operators Weight |
| Summary: | A well known open problem of Muckenhoupt-Wheeden says that any Calderón-Zygmund singular integral operator T is of weak type (1, 1) with respect to a couple of weights (w, Mw). In this paper we consider a somewhat “dual” problem: sup λ>0 λw x ∈ R n : |T f(x)| Mw > λ ≤ c Z Rn |f| dx. We prove a weaker version of this inequality with M3w instead of Mw. Also we study a related question about the behavior of the constant in terms of the A1 characteristic of w. |
|---|